The nucleosynthesis in asymptotic giant branch stars (briefly: AGB)is a challenging and fascinating subject in the theory of stellar evolution and important for observations as well. This is because about of half the heavy elements beyond iron are synthesized during thermal pulsation phases of these stars. Furthermore, the understanding of the production of the heavy elements and some light elements like carbon and fluorine represent a powerful tool to get more insight into the internal structure of these stars. The diversity of nuclear processing during the AGB phases may also motivate experimental activities in measuring important nuclear reactions. In this contribution, we emphasize several interesting feature of the nucleosynthesis in AGB stars which still needs further elaboration especially from theoretical point of view.